You don't want to store too much data in preferences (they're read synchronously at startup!)

Just having knowledge of the sqlite filename won't work since you whoever opens the database first will lock it. The easiest way to let other extensions do queries on your database is to expose the DB connection somewhere. That somewhere could be an XPCOM service component (this is how various toolkit services such as history, bookmarks, form data etc. do it, FWIW) or simply an object you import from a JavaScript module if you only want to consider JavaScript consumers.